Open In Colab

In [6]:
!pip install pandas

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In [7]:
import pandas as pd
import numpy as np

# Importar los datos
data = pd.read_csv("sample_data/ViZieR_cum_glob.tsv", delimiter="|")

# Filtrar los datos sin distancia al sol
data = data.dropna(subset=['Rsun'])

data.head()
Out[7]:
_RAJ2000 _DEJ2000 ID RAJ2000 DEJ2000 GLON GLAT Rsun Rgc Vt [Fe/H] SpT c Rh
0 6.021667 -72.080833 NGC 104 00 24 05.2 -72 04 51 305.90 -44.89 4.3 7.3 3.95 -0.76 G4 2.04 2.79
1 13.197917 -26.590000 NGC 288 00 52 47.5 -26 35 24 152.28 -89.38 8.1 11.4 8.09 -1.24 0.96 2.22
2 15.809583 -70.848333 NGC 362 01 03 14.3 -70 50 54 301.53 -46.25 8.3 9.2 6.40 -1.16 F9 1.94 0.81
3 48.063750 -55.216944 NGC 1261 03 12 15.3 -55 13 01 270.54 -52.13 16.0 17.9 8.29 -1.35 F7 1.27 0.75
4 53.345833 79.580556 Pal 1 03 33 23.0 +79 34 50 130.07 19.03 9.7 15.9 13.52 -0.80 1.50 0.48
In [8]:
# Chequear los tipos de datos
data.dtypes
Out[8]:
_RAJ2000    float64
_DEJ2000    float64
ID           object
RAJ2000      object
DEJ2000      object
GLON        float64
GLAT        float64
Rsun         object
Rgc          object
Vt           object
[Fe/H]       object
SpT          object
c            object
Rh          float64
dtype: object
In [9]:
# Convertir Rsun en un valor numérico para poder calcular
data['Rsun'] = pd.to_numeric(data['Rsun'], errors='coerce')
In [10]:
# Calcular las coordenadas usando radianes
data['x'] = data['Rsun'] * np.cos(np.radians(data['_RAJ2000'])) * np.cos(np.radians(data['_DEJ2000']))
data['y'] = data['Rsun'] * np.sin(np.radians(data['_RAJ2000'])) * np.cos(np.radians(data['_DEJ2000']))
data['z'] = data['Rsun'] * np.sin(np.radians(data['_DEJ2000']))
In [11]:
data.head()
Out[11]:
_RAJ2000 _DEJ2000 ID RAJ2000 DEJ2000 GLON GLAT Rsun Rgc Vt [Fe/H] SpT c Rh x y z
0 6.021667 -72.080833 NGC 104 00 24 05.2 -72 04 51 305.90 -44.89 4.3 7.3 3.95 -0.76 G4 2.04 2.79 1.315702 0.138789 -4.091414
1 13.197917 -26.590000 NGC 288 00 52 47.5 -26 35 24 152.28 -89.38 8.1 11.4 8.09 -1.24 0.96 2.22 7.051967 1.653753 -3.625584
2 15.809583 -70.848333 NGC 362 01 03 14.3 -70 50 54 301.53 -46.25 8.3 9.2 6.40 -1.16 F9 1.94 0.81 2.619976 0.741852 -7.840624
3 48.063750 -55.216944 NGC 1261 03 12 15.3 -55 13 01 270.54 -52.13 16.0 17.9 8.29 -1.35 F7 1.27 0.75 6.099960 6.789869 -13.141087
4 53.345833 79.580556 Pal 1 03 33 23.0 +79 34 50 130.07 19.03 9.7 15.9 13.52 -0.80 1.50 0.48 1.047272 1.407372 9.540048
In [12]:
# Calcular la posición promedio del centro
x_avg = data['x'].mean()
y_avg = data['y'].mean()
z_avg = data['z'].mean()
In [13]:
x_avg, y_avg, z_avg
Out[13]:
(-1.8773897807955038, -5.20959303904406, -3.5349928267690482)
In [14]:
# Distancia al centro
center_distance = np.sqrt(x_avg**2 + y_avg**2 + z_avg**2)
center_distance
Out[14]:
6.569674748935471
In [15]:
# Calcular la distancia de cada cúmulo al centro de la Galaxia

import math

def calculate_distance(x1, y1, z1, x2, y2, z2):
    delta_x = x2 - x1
    delta_y = y2 - y1
    delta_z = z2 - z1

    sum_of_squares = delta_x ** 2 + delta_y ** 2 + delta_z ** 2
    distance = math.sqrt(sum_of_squares)

    return distance

data['distance_to_gal_center'] = data.apply(
    lambda row: calculate_distance(
        row['x'],
        row['y'],
        row['z'],
        x_avg,
        y_avg,
        z_avg
    ),
    axis=1
)
In [16]:
data.head()
Out[16]:
_RAJ2000 _DEJ2000 ID RAJ2000 DEJ2000 GLON GLAT Rsun Rgc Vt [Fe/H] SpT c Rh x y z distance_to_gal_center
0 6.021667 -72.080833 NGC 104 00 24 05.2 -72 04 51 305.90 -44.89 4.3 7.3 3.95 -0.76 G4 2.04 2.79 1.315702 0.138789 -4.091414 6.253849
1 13.197917 -26.590000 NGC 288 00 52 47.5 -26 35 24 152.28 -89.38 8.1 11.4 8.09 -1.24 0.96 2.22 7.051967 1.653753 -3.625584 11.262644
2 15.809583 -70.848333 NGC 362 01 03 14.3 -70 50 54 301.53 -46.25 8.3 9.2 6.40 -1.16 F9 1.94 0.81 2.619976 0.741852 -7.840624 8.613040
3 48.063750 -55.216944 NGC 1261 03 12 15.3 -55 13 01 270.54 -52.13 16.0 17.9 8.29 -1.35 F7 1.27 0.75 6.099960 6.789869 -13.141087 17.317686
4 53.345833 79.580556 Pal 1 03 33 23.0 +79 34 50 130.07 19.03 9.7 15.9 13.52 -0.80 1.50 0.48 1.047272 1.407372 9.540048 14.943044
In [17]:
# RA y DEC de una estrella en Sagitario.
# Por ejemplo Alnasl (Gamma Sagittarii)
# RA=18h, DEC=-30°
# https://en.wikipedia.org/wiki/Gamma2_Sagittarii
RA_star = 18 * 15  # Convertir a grados
DE_star = -30

RA_star_rad = np.deg2rad(RA_star)
DE_star_rad = np.deg2rad(DE_star)

x_star = center_distance * np.cos(RA_star_rad) * np.cos(DE_star_rad)
y_star = center_distance * np.sin(RA_star_rad) * np.cos(DE_star_rad)
z_star = center_distance * np.sin(DE_star_rad)
In [18]:
print(f"Posición de Alnasl (Gamma Sagittarii) en Sagitario: {x_star, y_star, z_star}")

Posición de Alnasl (Gamma Sagittarii) en Sagitario: (-1.0451451547795845e-15, -5.689505227179272, -3.284837374467735)
In [19]:
"""
Parece estar cerca del centro de la galaxia.
"""
Out[19]:
'\nParece estar cerca del centro de la galaxia.\n'
In [20]:
# Radio del cúmulo en parsecs
# Suponiendo que Rh está en minutos de arco
data['radio_parsecs'] = data['Rsun'] * np.tan(np.deg2rad(data['Rh'] / 60)) * 1000
radio_promedio = data['radio_parsecs'].mean()
In [21]:
data.head()
Out[21]:
_RAJ2000 _DEJ2000 ID RAJ2000 DEJ2000 GLON GLAT Rsun Rgc Vt [Fe/H] SpT c Rh x y z distance_to_gal_center radio_parsecs
0 6.021667 -72.080833 NGC 104 00 24 05.2 -72 04 51 305.90 -44.89 4.3 7.3 3.95 -0.76 G4 2.04 2.79 1.315702 0.138789 -4.091414 6.253849 3.489787
1 13.197917 -26.590000 NGC 288 00 52 47.5 -26 35 24 152.28 -89.38 8.1 11.4 8.09 -1.24 0.96 2.22 7.051967 1.653753 -3.625584 11.262644 5.230752
2 15.809583 -70.848333 NGC 362 01 03 14.3 -70 50 54 301.53 -46.25 8.3 9.2 6.40 -1.16 F9 1.94 0.81 2.619976 0.741852 -7.840624 8.613040 1.955641
3 48.063750 -55.216944 NGC 1261 03 12 15.3 -55 13 01 270.54 -52.13 16.0 17.9 8.29 -1.35 F7 1.27 0.75 6.099960 6.789869 -13.141087 17.317686 3.490659
4 53.345833 79.580556 Pal 1 03 33 23.0 +79 34 50 130.07 19.03 9.7 15.9 13.52 -0.80 1.50 0.48 1.047272 1.407372 9.540048 14.943044 1.354376
In [22]:
print("RESUMEN")
print(f"Posición promedio del centro: {x_avg, y_avg, z_avg}")
print(f"Distancia del Sol al centro: {center_distance} kpc")
print(f"Posición de Alnasl (Gamma Sagittarii) en Sagitario: {x_star, y_star, z_star}")
print(f"Radio promedio de los cúmulos en parsecs: {radio_promedio}")

RESUMEN
Posición promedio del centro: (-1.8773897807955038, -5.20959303904406, -3.5349928267690482)
Distancia del Sol al centro: 6.569674748935471 kpc
Posición de Alnasl (Gamma Sagittarii) en Sagitario: (-1.0451451547795845e-15, -5.689505227179272, -3.284837374467735)
Radio promedio de los cúmulos en parsecs: 4.434517864178317
In [23]:
"""
Trataré de graficar los cúmulos, el Sol y el centro de la Galaxia.
"""
Out[23]:
'\nTrataré de graficar los cúmulos, el Sol y el centro de la Galaxia.\n'
In [24]:
!pip install matplotlib

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You should consider upgrading via the '/Users/daiangan/Python Virtual Environments/venv_dataspell1/bin/python -m pip install --upgrade pip' command.
In [25]:
import matplotlib.pyplot as plt

fig = plt.figure(figsize=(10, 8))
ax = fig.add_subplot(111, projection='3d')

# Graficar los cúmulos
ax.scatter(
    data['x'],
    data['y'],
    data['z'],
    c='green',
    marker='o',
    s=data['radio_parsecs'],
    alpha=0.5,
    label='Cúmulos globulares'
)

# Marcar el punto estimado del centro de la galaxia
ax.scatter(x_avg, y_avg, z_avg, c='red', marker='o', s=100, label='Centro estimado de la galaxia')

# Marcar la posición del Sol
ax.scatter(0, 0, 0, c='yellow', marker='o', s=100, label='Sol')

# Alnasl (Gamma Sagittarii)
ax.scatter(x_star, y_star, z_star, c='blue', marker='*', s=100, label='Alnasl (Gamma Sagittarii)')

# Etiquetas y título
ax.set_xlabel('X (kpc)')
ax.set_ylabel('Y (kpc)')
ax.set_zlabel('Z (kpc)')
ax.set_title('Distribución de cúmulos globulares en relación con el Sol y el centro de la galaxia')
ax.legend()

# Adjust Y axis limits
y_min = -20  # Example value
y_max = 20   # Example value
ax.set_ylim(y_min, y_max)

# Adjust view
ax.view_init(elev=20, azim=-20)

# Mostrar el gráfico
plt.show()
In [26]:
!pip install plotly

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You should consider upgrading via the '/Users/daiangan/Python Virtual Environments/venv_dataspell1/bin/python -m pip install --upgrade pip' command.
In [27]:
# Normalize radio
valid_radio_parsecs = [size if not np.isnan(size) else 5 for size in data['radio_parsecs']]
In [28]:
import plotly.graph_objects as go

fig = go.Figure()

# Los cúmulos
fig.add_trace(go.Scatter3d(
    x=data['x'], y=data['y'], z=data['z'],
    mode='markers',
    marker=dict(
        size=valid_radio_parsecs,
        color='green',
        opacity=0.5,
    ),
    text=data['ID'],
    hoverinfo="text",
    name='Cúmulos globulares'
))

# Centro estimado de la galaxia
fig.add_trace(go.Scatter3d(
    x=[x_avg], y=[y_avg], z=[z_avg],
    mode='markers',
    marker=dict(size=5, color='red', opacity=1),
    name='Centro estimado de la galaxia'
))

# Sol
fig.add_trace(go.Scatter3d(
    x=[0], y=[0], z=[0],
    mode='markers',
    marker=dict(size=5, color='yellow', opacity=1),
    name='Sol'
))

# Alnasl (Gamma Sagittarii)
fig.add_trace(go.Scatter3d(
    x=[x_star], y=[y_star], z=[y_star],
    mode='markers',
    marker=dict(size=5, color='blue', opacity=1),
    name='Alnasl (Gamma Sagittarii)'
))

fig.update_layout(
    margin=dict(l=0, r=0, b=0, t=0),
    scene=dict(
        xaxis_title='X (kpc)',
        yaxis_title='Y (kpc)',
        zaxis_title='Z (kpc)'
    ),
    title='Distribución de cúmulos globulares en relación con el Sol y el centro de la galaxia'
)

fig.show()
In [29]:
# Plot histogram based on radio

import plotly.express as px

fig = px.histogram(data['radio_parsecs'])

fig.show()
In [30]:
# Plot relation between radio and distance to center of the Galaxy

fig = px.scatter(data,
                 x='distance_to_gal_center',
                 y='radio_parsecs',
                 hover_name='ID',
                 title='Relación entre distancia al centro de la galaxia y radio del cúmulo',
                 labels={
                     'distance_to_gal_center': 'Distancia al centro de la galaxia',
                     'radio_parsecs': 'Radio del cúmulo'
                 }
)

fig.show()